A and B can do a work in 45 days and 40 days respectively. They started working but A left after some days and B alone complete the remaining work in 23 days. After how many days did A leave ?

9

A can do a work in time = 45 days

A's one day work = 1/45

B can do a work in time = 40 days

B's one day work = 1/40

If they work together, one day work of A and B = 1/45 + 1/40 = 8+9/360 = 17/360

Let they work for x days initially,

A and B x days work = 17x/360

Remaining work = 1- 17x/360 = (360-17x)/360

B alone does (360-17x)/360 in time = 23 days

Also, B's 23 days work = 23/40

⇒ (360-17x)/360 = 23/40

360-17x = 9*23

17x = 360-207

x = 153/17 = 9 days

The correct answer is option (4) : 9